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MATH 211 Lecture Notes - Lecture 12: Ellipse, Sine Wave, Quadric

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champagnefrog144

12 Sep 2016

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MATH - Mathematics

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William F.Bertolette

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Learning objective: the learner will be able to (1) recognize, write, and graph equations of cylindrical surfaces; (2) recognize, write, and graph equations of quadric surfaces. So far, you have studied lines, planes, and spheres in space. A line in space is represented by the parametric equations, (cid:1876)=(cid:1876)0+(cid:1853),(cid:1877)= (cid:1877)0+(cid:1854),(cid:1878)=(cid:1878)0+(cid:1855), where (cid:1876)0,(cid:1877)0,(cid:1878)0 is a point on the line and = (cid:1853),(cid:1854),(cid:1855) is a vector parallel to the line. A plane is represented by the equation, (cid:1853) (cid:1876) (cid:1876)0 +(cid:1854) (cid:1877) (cid:1877)0 +(cid:1855) (cid:1878) (cid:1878)0 =(cid:882), where (cid:1876)0,(cid:1877)0,(cid:1878)0 is a point on the plane and = (cid:1853),(cid:1854),(cid:1855) is a vector normal to the plane. A sphere is represented by the equation, (cid:1876) (cid:1876)0 2+ (cid:1877) (cid:1877)0 2+ (cid:1878) (cid:1878)0 2=2, where (cid:1876)0,(cid:1877)0,(cid:1878)0 is the center of the sphere and r is the radius of the sphere. A third type of surface in space is called a cylindrical surface, or simply a cylinder.

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